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Controlling Homoclinic Orbits

Bloch, A. M. and Marsden, J. E. (1989) Controlling Homoclinic Orbits. Theoretical and Computational Fluid Dynamics, 1 (3). pp. 179-190. ISSN 0935-4964. doi:10.1007/BF00417919.

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In this paper we analyze various control-theoretic aspects of a nonlinear control system possessing homoclinic or heteroclinic orbits. In particular, we show that for a certain class of nonlinear control system possessing homoclinic orbits, a control can be found such that the system exhibits arbitrarily long periods in a neighborhood of the homoclinic. We then apply these ideas to bursting phenomena in the near wall region of a turbulent boundary layer. Our analysis is based on a recently developed finite-dimensional model of this region due to Aubry, Holmes, Lumley, and Stone.

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Additional Information:© 1989 Springer-Verlag Berlin Heidelberg. Communicated by John Lumley. We would like to thank P. Holmes, J. Lumley, Emily Stone, and Steve Wiggins for their useful comments. The research of A.M. Bloch was partially supported by the U.S. Army Research Office through MSI at Cornell University and by NSF Grant DMS-8701576 and AFOSR Grant AFOSR-ISSA-87-0077, J.E. Marsden's research was partially supported by DOE Contract DE-AT03-88ER-12097 and MSI at Cornell University and by AFOSR Contract No. 88-NA-321.
Funding AgencyGrant Number
Army Research Office (ARO)UNSPECIFIED
Air Force Office Scientific Research (AFOSR)ISSA-87-0077
Department of Energy (DOE)DE-AT03-88ER-12097
Air Force Office Scientific Research (AFOSR)88-NA-321
Issue or Number:3
Record Number:CaltechAUTHORS:20101012-090636565
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20393
Deposited By: Ruth Sustaita
Deposited On:05 Nov 2010 16:46
Last Modified:08 Nov 2021 23:59

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